$$ \begin{aligned} 5(x+3) &= 3\cdot(4+2x)&& \text{simplify left and right hand side} \\[1 em]5x+15 &= 12+6x&& \\[1 em]5x+15 &= 6x+12&& \text{move the $ \color{blue}{ 6x } $ to the left side and $ \color{blue}{ 15 }$ to the right} \\[1 em]5x-6x &= 12-15&& \text{simplify left and right hand side} \\[1 em]-x &= -3&& \text{switch signs on both sides} \\[1 em]x &= 3&& \\[1 em] \end{aligned} $$

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